scholarly journals A New Generating Family of Distributions: Properties and Applications to the Weibull Exponential Model

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
El-Sayed A. El-Sherpieny ◽  
Salwa Assar ◽  
Tamer Helal
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Exponential Model ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Set ◽  
Rate Functions ◽  
Family Of Distributions

A new method for generating family of distributions was proposed. Some fundamental properties of the new proposed family include the quantile, survival function, hazard rate function, reversed hazard and cumulative hazard rate functions are provided. This family contains several new models as sub models, such as the Weibull exponential model which was defined and discussed its properties. The maximum likelihood method of estimation is using to estimate the model parameters of the new proposed family. The flexibility and the importance of the Weibull-exponential model is assessed by applying it to a real data set and comparing it with other known models.

scholarly journals A New Extension of Lindley Geometric Distribution and its Applications

2019 ◽  
pp. 249-263
Author(s):  
I. Elbatal ◽  
Mohamed G. Khalil
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Geometric Distribution ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Distribution

A new four-parameter distribution called the beta Lindley-geometric distribution is proposed. The hazard rate function of the new model can be constant, decreasing, increasing, upside down bathtub or bathtub failure rate shapes. Various structural properties including of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated using a real data set.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals Discretization of the method of generating an expanded family of distributions based upon truncated distributions

2021 ◽  
Vol 25 (Spec. issue 1) ◽  
pp. 19-30
Author(s):  
Muhammad Farooq ◽  
Muhammad Mohsin ◽  
Muhammad Naeem ◽  
Muhammad Farman ◽  
Ali Akgul ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Survival Function ◽  
Real Data ◽  
Reliability Function ◽  
Continuous Functions ◽  
Discrete Distributions ◽  
Discrete Version ◽  
Model Parameters ◽  
Data Set ◽  
Family Of Distributions

Discretization translates the continuous functions into discrete version making them more adaptable for numerical computation and application in applied mathematics and computer sciences. In this article, discrete analogues of a generalization method of generating a new family of distributions is provided. Several new discrete distributions are derived using the proposed methodology. A discrete Weibull-Geometric distribution is considered and various of its significant characteristics including moment, survival function, reliability function, quantile function, and order statistics are discussed. The method of maximum likelihood and the method of moments are used to estimate the model parameters. The performance of the proposed model is probed through a real data set. A comparison of our model with some existing models is also given to demonstrate its efficiency.

scholarly journals Truncated Weibull-G More Flexible and More Reliable than Beta-G Distribution

2017 ◽  
Vol 6 (5) ◽  
pp. 1 ◽  
Author(s):  
Hossein Najarzadegan ◽  
Mohammad Hossein Alamatsaz ◽  
Saied Hayati
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Stochastic Comparison ◽  
Data Set ◽  
New Family ◽  
Rate Functions

Our purpose in this study includes introducing a new family of distributions as an alternative to beta-G (B-G) distribution with flexible hazard rate and greater reliability which we call Truncated Weibull-G (TW-G) distribution. We shall discuss several submodels of the family in detail. Then, its mathematical properties such as expansions, probability density function and cumulative distribution function, moments, moment generating function, order statistics, entropies, unimodality, stochastic comparison with the B-G distribution and stress-strength reliability function are studied. Moreover, we study shape of the density and hazard rate functions, and based on the maximum likelihood method, estimate parameters of the model. Finally, we apply the model to a real data set and compare B-G distribution with our proposed model.

Extended exponentiated Nadarajah-Haghighi model: Mathematical properties, characterizations and applications

2018 ◽  
Vol 55 (4) ◽  
pp. 498-522
Author(s):  
Morad Alizadeh ◽  
Mahdi Rasekhi ◽  
Haitham M. Yousof ◽  
Thiago G. Ramires ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Survival Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Failure Rate Function ◽  
Data Set ◽  
Mathematical Properties

In this article, a new four-parameter model is introduced which can be used in mod- eling survival data and fatigue life studies. Its failure rate function can be increasing, decreasing, upside down and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and exibility of the new model in modeling a real data set.

scholarly journals A Flexible Extension to an Extreme Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 745
Author(s):  
Mohamed S. Eliwa ◽  
Fahad Sameer Alshammari ◽  
Khadijah M. Abualnaja ◽  
Mahmoud El-Morshedy
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Hazard Rate Function ◽  
Censored Samples ◽  
Extreme Distribution ◽  
Extreme Model

The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

scholarly journals The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

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